Just did mine on a GE JVM1642. Four screws had to be removed: two screws that hold the handle to the trim, and two screws that hold the handle to the metal frame. The inside and the outside trim had to be removed to get to the four screws.
I loosened the inside trim to get to the screws that hold the handle to the metal frame. I could not get the trim off completely (it stayed attached near the hinges) but it was ok because I could reach the 2 screws in the handle. I used a small putty knife that I slipped in between the trim and the grid portion and/or the outside trim. I felt for the four latches (top and bottom) and the couple of latches on the handle side of the door. I did not want to break a trim piece so I took extra care on how far I bent it back.
When I got the inside trim off enough, I removed the screws that I could reach.
Then I removed the outside trim using the putty knife. The outside trim uses plastic latches to attach to the metal door frame. My latch and its spring popped off. I had to reattach after the front trim was back on.
When the outside trim is off, I replaced the handle using TWO screws (and not the two screws that can be reached from the inside! Those are installed later). I reversed the process to put it back together.
I took special care not to lean/torque or otherwise mess with the metal grid frame.
Your microwave may be different so these instructions may not be accurate (i.e. your mileage may vary). | 
